how to compute the slope of the riser for steps on a deck

Question

if the height of a deck (porch) is 21 inches and the builder wants the steps to extend out from the deck (porch) 4 feet, how do you compute the rise that each step should be built?

Answer 1

Start with just one step. The riser would be 21" and the tread 48" or 4'.

With 2 steps, the riser 4 would be 21/2 and the tread 48/2.

With n steps, the riser would be 21/n and the tread 48/n.

So the calculation depends on the number of steps.

To fit the average foot comfortably on to the tread the tread would be about 12". 48/n=12 so n=4.

If n=4 then the riser is 21/4=5.25". To make the riser shorter requires a corresponding shortening of the tread. For a 6" tread, for example, n=8 and the riser is 2.625".